Scala analysis: 628_T35
Aristoxenian style tetrachord 6.5 + 6.5 + 17, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 108.333 cents 108.333330 2: 216.667 cents 216.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 283.3333 cents 283.3333 1: 108.3333 cents 108.3333 2: 108.3333 cents 108.3333 3: 283.3333 cents 283.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 108.33333 cents 1: 1 283.33333 cents 2: 1 216.66667 cents 2: 2 391.66667 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 108.3 216.7 500.0 108.3: 108.3 391.7 500.0 216.7: 283.3 391.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 108.3333 .. 283.3333 cents 175.00000 cents 108.33333 cents 2: 216.6667 .. 391.6667 cents 175.00000 cents -66.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 108.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 283.33333 cents Average / Smallest step : 1.538462 Largest / Average step : 1.700000 Largest / Smallest step : 2.615385 Median interval of one step : 108.33333 cents, amount: 2 Most common interval of one step : 108.33333 cents, amount: 2 Least squares average step : 145.83333 cents, oct.: 437.50000 cents Scale is not proper Scale has Myhill's property chromas: 175.00000 cents and 66.66667 cents, ratio: 2.625000 generators: 1 of 108.33333 cents and 391.66667 cents ET pair of linear temperament : 28&46 Scale is distributional even Scale is a mode of a 60-tone equal temperament with octave 500.000 cents degrees: 13 26 60 generators: 13 and 47 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.66666 cents Scale diversity : 1.117221 Lumma stability : 0.433333 Lumma impropriety factor : 0.133333 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 66.66666 cents Most common intervals : 108.33333 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 68.8866 c. M: 108.3333 c. 4: 1 1 2 P M ME S SD: 21.5166 c. M:-33.3333 c. 5: 1 1 3 N M DE S SD: 10.7583 c. M: 16.6667 c. 9: 2 2 5 N M DE S SD: 3.5861 c. M:-5.5556 c. 14: 3 3 8 N M DE S SD: 1.5369 c. M: 2.3810 c. 23: 5 5 13 N M DE S SD: 0.4678 c. M:-0.7246 c. 37: 8 8 21 N M DE S SD: 0.2908 c. M: 0.4505 c. 60: 13 13 34 N M DE S SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 64.4287 cents 6 x 7:8 S SD: 25.1211 cents 7 x 8:9 S SD: 33.2586 cents 8 x 9:11 SD: 26.4399 cents 9 x 10:12 S SD: 17.1593 cents 10 x 11:13 SD: 34.5158 cents 11:12 x 15 S SD: 28.0845 cents 12:13:14:16 S SD: 19.5468 cents 13:14:15:17 SD: 17.0932 cents 14:15:16:19 SD: 11.3374 cents 15:16:17:20 SD: 1.3068 cents 126:134:143:168 SD: 1.1970 cents 141:150:160:188 SD: 1.0577 cents 143:152:162:191 SD: 0.9848 cents 156:166:177:208 SD: 0.9616 cents 158:168:179:211 SD: 0.7722 cents 173:184:196:231 SD: 0.5983 cents 188:200:213:251 SD: 0.4548 cents 203:216:230:271 SD: 0.3370 cents 218:232:247:291 SD: 0.2436 cents 233:248:264:311 SD: 0.1785 cents 248:264:281:331 SD: 0.1514 cents